TY - JOUR
T1 - A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities
AU - Ammari , Kaïs
AU - Choulli , Mourad
AU - Triki , Faouzi
JO - CSIAM Transactions on Applied Mathematics
VL - 2
SP - 207
EP - 239
PY - 2020
DA - 2020/07
SN - 1
DO - http://doi.org/10.4208/csiam-am.2020-0001
UR - https://global-sci.org/intro/article_detail/csiam-am/17176.html
KW - Evolution equations, Laplace-Beltrami operator, observability inequality, geometric
control, initial-to-boundary operator.
AB - <p style="text-align: justify;">We survey some of our recent results on inverse problems for evolution
equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown
coefficients from boundary measurements by varying initial conditions. Based on observability inequalities and a special choice of initial conditions, we provide uniqueness and stability estimates for the recovery of volume and boundary lower order coefficients in wave and heat equations. Some of the results presented here are slightly
improved from their original versions.</p>